Z-index is a chronically buggy issue that can relate to the render order of objects erroneously in most browsers. I ran into the same problem, try setting the drop down elements to a z-index of 10000 or so. The number should be huge, because depending on the rendering errors occurring it needs to at least be larger that the total number of DOM objects in the page. I could go more in depth here but z-index=10000 or higher should solve your problem. If it doesn't work on the first try be sure to set the containing element that is a sibling to the twitter widget to a z-index of 10000 as well.
[edited by: bill at 8:54 am (utc) on May 18, 2010] [edit reason] No signatures or links to your site. See TOS. [/edit]